The speed of a boat in still water is 15 km / hr and the rate of current is 3 km / hr. The distance travelled downstream in 12 minutes is

Options

A. (a)1.2 km
B. (b)1.8 km
C. (c)2.4 km
D. (d)3.6 km

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the Speed of the Boat Downstream
The speed of the boat in still water is given as 15 km/hr, and the speed of the current is 3 km/hr. When the boat is moving downstream, the speeds add up.

**Formula:**
\[ \text{Speed downstream} = \text{Speed of boat} + \text{Speed of current} \]

**Calculation:**
\[ \text{Speed downstream} = 15 \, \text{km/hr} + 3 \, \text{km/hr} = 18 \, \text{km/hr} \]

### Step 2: Convert Time from Minutes to Hours
The time given is 12 minutes. To use the speed in km/hr, we need to convert this time into hours.

**Conversion:**
\[ \text{Time in hours} = \frac{12 \, \text{minutes}}{60} = \frac{1}{5} \, \text{hours} \]

### Step 3: Calculate the Distance Travelled Downstream
Now that we have the speed downstream and the time in hours, we can calculate the distance travelled using the formula:

**Formula:**
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

**Calculation:**
\[ \text{Distance} = 18 \, \text{km/hr} \times \frac{1}{5} \, \text{hr} = \frac{18}{5} \, \text{km} = 3.6 \, \text{km} \]

### Final Answer
The distance travelled downstream in 12 minutes is **3.6 km**.

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